Posted by: captainfalcon | April 13, 2010

Of Mint and Jelly

Let’s say you have $1.00 to spend on jelly. Say, further, that strawberry jelly isn’t twice as good as grape jelly. Finally, assume that grape jelly costs $0.50, and strawberry jelly costs $1.00.  Necessarily, your choices are: (1) buy two grape jellies, (2) buy one strawberry jelly or (3) buy one grape jelly and do x with the remaining $0.50.

One could argue that it is never rational to opt for (2) along the following lines. Strawberry jelly isn’t twice as good as grape jelly. That means it isn’t worth twice as much as grape jelly. If it isn’t worth twice as much as grape jelly then you oughtn’t to pay twice as much for it. But opt for (2) and you do that. So it isn’t rational to opt for (2).

But imagine this scenario. You have a desire of strength 0.9s for strawberry jelly. You have a desire of strength 0.5s for grape jelly. You have a desire of strength 0.6s for two grape jellies. And you have a desire of strength 0.7s for grape jelly and $0.50 in your pocket.

This scenario seems possible (that is, I don’t see any contradictions in it). The law of diminishing returns (or whatever) explains how one can desire grape jelly with 0.6s and two grape jellies with 0.7s. And we can make sense of the final claim about a 0.7s desire for grape jelly plus $0.50. What it predicts, ceteris paribus, is that you would put in slightly less effort (20% less) to go grab a bundle consisting in grape jelly and $0.50 than you would to grab a bundle consisting in strawberry jelly. Likewise, the claim that your desire for grape jelly is slightly less than one half your desire for strawberry jelly predicts, ceteris paribus, you’d put in slightly under double the effort to go get it.

But notice that, in the scenario described, it is rational (assuming your desires are properly grounded) to opt for (2). You most strongly desire that outcome.

So what’s wrong with the argument in paragraph two? I think it’s with the move from strawberry jelly isn’t twice as good as grape jelly to strawberry jelly isn’t worth twice as much as grape jelly. That move isn’t licensed, what’s licensed is the move from strawberry jelly isn’t twice as good as grape jelly to one doesn’t (or shouldn’t) have a desire for strawberry jelly that’s twice as strong as one’s desire for grape jelly. Unlike the claim about its (monetary) worth, this claim doesn’t have an immediate implication about how much you’d pay for it.

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Responses

  1. I agree that it doesn’t necessarily follow that if strawberry jelly is not twice as good as grape jelly one should not prefer to pay twice as much, as the scenerio you outlined above is clearly consistent with the preconditions. I would say that a) it is also not necessarily true that if one has a preference for strawberry jelly that one should be willing twice as much for it and b) I suspect if you collated all reasonable dispositions towards the three bundles given that you do not like strawberry jelly twice as much as grape and it costs twice as much, it is more likely that you would prefer one of the two grape bundles over the strawberry bundle.

  2. (b) is probably false. (a) is not even false.

  3. My apologies that there is no grammar check in comments. I am sorry I let you down so.

  4. How would a grammar checker have saved you from your substantive, non-grammatical, mistakes?


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